Egypt is being described as a nation on the brink of a volcano, as protesters again march across the country, this time demanding President Mohamed Morsy step down by Tuesday. And the army has warned both the president and the opposition to resolve their differences and "meet the people's demands" within 48 hours -- or, the army says, it will step in.

As the clock ticks down on those deadlines CNN's senior international correspondent Ben Wedeman in Cairo, Egypt, explains to Christiane Amanpour what's behind the latest protests and what the military can do.

Amanpour: How are the people reacting to the military ultimatum?

Wedeman: The people in Tahrir Square are reacting quite positively. In fact, as this statement was being issued on Egyptian TV, we heard repeated cheers coming from the crowd.

And since that announcement was made, we've had more and more people coming into the square.

Egyptian military helicopters flew overhead with flags underneath -- a very clear signal from the military that they sympathize with the people in the square. At least that's how it's been interpreted here.

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So, a very enthusiastic response from most of them. Some of them worry that we're really just going to go back to February 12, 2011, when the military was in control and in control for almost 18 months afterwards. That period saw frequent clashes. But certainly at the moment, these people here quite happy with the military's statement.

Amanpour: Why do they think the military is on their side? It called for both the president and the opposition to resolve their differences and also what do you read into the military's declaration?

Wedeman: Well, as far as the military goes, many Egyptians look at it as the strongest institution in Egypt -- the institution that, above politics, can impose order... That explains why so many people are enthusiastic.

Now if you look carefully at the military's statement, it's clear they're losing their confidence in President Morsy. They see that he has huge opposition in the streets. The counter-demonstrations supporting President Morsy are much smaller.

Now where does it go from here is not altogether clear. The military really has told not just President Morsy, but the opposition: 'You've got to get your act together.'

It's going to be difficult for both the opposition and President Morsy to deal with their bases, and one another, to try to meet the army's very clear demand.

Amanpour: The opposition is incredibly fragmented and definitely not unified, neither with their message or their different sides. But what do we expect from the presidency?

Wedeman: The Muslim Brotherhood has said that they are studying this statement by the army. That might not be what the army wanted to hear from them. But within the movement itself, there's a danger of a real split because it's important to keep in mind that the Muslim Brotherhood had a series of electoral victories culminating in President Morsy's election in June last year.

That was a historic opportunity where the biggest, the best organized and the oldest Islamist movement took power -- a chance to show it can rule. And now they suddenly see this experiment slipping between their fingers as millions of Egyptians, it seems, come out in the street in clear rejection of the project of the Muslim Brotherhood.

Egyptians are saying this is not us. This is not our identity... It's a Wahhabi identity from Saudi Arabia. And many people in the square will tell you "We are Egyptians. That is our identity. We are Muslims; we are Christians. But we're Egyptians before anything else."

Amanpour: What do you think about the complaints from the president and others about the organized opposition from the very beginning from Mubarak-era ministers and institutions that still existed, to an extent?

Wedeman: Well, there's no question that the job of running Egypt today as president has got to be one of the most difficult jobs on Earth. The Muslim Brotherhood, for years, was persecuted, pursued, jailed, tortured and then sometimes killed by the regimes in power in Egypt.

They won an election. They took over as head of state. And they suddenly found that much of the bureaucracy, the police in particular, to a lesser extent the army, the ministries, the local governorates were opposed to them.

They were afraid that they would impose their people from the Muslim Brotherhood on every level of the bureaucracy.

So you had a severe pushback from all of these. And the police are a classic example. The police were the tip of the spear in the war of the Egyptian state against the Muslim Brotherhood.

On Monday, the headquarters of the Muslim Brotherhood was attacked, trashed, scorched, burned and defaced, and then the police came to guard the ruins.

So if you're president of Egypt and you can't trust your police and you're not sure about the army and you know that the bureaucracy doesn't like you, you're going to have a very difficult job at running this very complicated country.